Problem 26 - College Algebra

Question

Find each product. $$(2 x-5)(7 x+2)$$

Step-by-Step Solution

Answer

The product of the two binomials \((2 x-5)(7 x+2)\) is \(14x^2 - 31x - 10\)

Step 1: Multiply the First Terms

Multiply the 'first' terms in each binomial. This means you multiply the 2x in the first binomial by the 7x in the second binomial. This results in a product of \(14x^2\).

Step 2: Multiply the Outer Terms

Next, multiply the 'outer' terms. Here, the outer terms are 2x from the first binomial and 2 from the second binomial, which gives us a product of \(4x\).

Step 3: Multiply the Inner Terms

The 'inner' terms are -5 from the first binomial and 7x from the second binomial. The product of these terms is \(-35x\).

Step 4: Multiply the Last Terms

The last terms are -5 from the first binomial and 2 from the second binomial. Their product is \(-10\).

Step 5: Combine Like Terms

Now add up the four terms. \(14x^2 + 4x - 35x -10\). We can combine the middle two terms to simplify this to \(14x^2 - 31x - 10\).